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Related Concept Videos

Coefficient of Correlation01:12

Coefficient of Correlation

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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
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Calibration Curves: Correlation Coefficient01:10

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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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Calculating and Interpreting the Linear Correlation Coefficient01:11

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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
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Correlations02:20

Correlations

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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Correlation and Causation01:27

Correlation and Causation

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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
Correlation versus Causation
If the dependent variable increases or decreases when the independent variable increases, there is a positive or negative...
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Coefficient of Variation01:10

Coefficient of Variation

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The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...
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Divergence of Root Microbiota in Different Habitats based on Weighted Correlation Networks
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Clustering Coefficients for Correlation Networks.

Naoki Masuda1, Michiko Sakaki2,3, Takahiro Ezaki4

  • 1Department of Engineering Mathematics, University of Bristol, Bristol, United Kingdom.

Frontiers in Neuroinformatics
|March 31, 2018
PubMed
Summary
This summary is machine-generated.

We developed new clustering coefficients for brain network analysis using correlation matrices. These novel measures better capture age-related changes in brain networks compared to traditional methods.

Keywords:
agingclustering coefficientfunctional connectivitynetwork neurosciencepartial correlationpartial mutual information

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Area of Science:

  • Neuroscience
  • Network Science
  • Graph Theory
  • Brain Imaging Analysis

Background:

  • Graph theory is crucial for understanding brain networks, with clustering coefficients quantifying local network structure.
  • Existing clustering coefficient measures face challenges when applied to correlation-based brain networks, particularly regarding pseudo-correlations and data thresholding.
  • Accurate measurement of network properties is essential for understanding how factors like age and cognitive state affect brain organization.

Purpose of the Study:

  • To propose novel clustering coefficients specifically designed for correlation matrices representing brain networks.
  • To address limitations of conventional clustering coefficients, including issues with thresholding, negative correlations, and pseudo-correlations.
  • To evaluate the utility of these new measures in characterizing age-related changes in functional brain networks.

Main Methods:

  • Developed clustering coefficients utilizing three-way partial correlation or partial mutual information to assess node associations.
  • Applied the proposed methods to functional magnetic resonance imaging (fMRI) data from healthy participants across various age groups.
  • Compared the performance of the novel clustering coefficients against conventional measures in relation to age and node connectivity.

Main Results:

  • The proposed clustering coefficients demonstrate a decline with increasing age in functional brain networks.
  • Novel coefficients show a stronger correlation with age than conventional clustering coefficients.
  • Local variants of the proposed coefficients effectively characterize individual nodes without being confounded by overall connectivity, unlike conventional local measures.

Conclusions:

  • The proposed clustering coefficients offer a more robust and sensitive method for analyzing correlational brain networks.
  • These new measures provide valuable insights into age-related alterations in brain network clustering.
  • The findings are expected to advance the understanding of network dynamics in functional time series and across-participant correlations in neuroimaging studies.